(2x)yz=2(xy)z property statement
Associate property statement of Muliplcation
Communcation property of mutlipcation
The (2x)yz=2(xy)z property statement states that for any values of x, y, and z, if both sides are simplified, they will be equal to each other.
The associative property of multiplication states that the grouping of factors does not affect the product. In other words, for any values of a, b, and c,
a(bc)=(ab)c.
The communicative property of multiplication states that the order of factors does not affect the product. In other words, for any values of a and b,
ab=ba.
The property statement (2x)yz = 2(xy)z refers to the associative property of multiplication. According to this property, when three or more numbers are multiplied together, the grouping of the factors does not affect the result.
The associative property of multiplication is stated as:
For any three numbers a, b, and c,
(a * b) * c = a * (b * c)
In the given property statement (2x)yz = 2(xy)z, it implies that the numbers 2x, y, and z are being multiplied together. It doesn't matter if we multiply (2x) with y first or multiply yz first, as the result will be the same. This is because of the associative property of multiplication.
To confirm that (2x)yz = 2(xy)z is an example of the associative property of multiplication, let's go through the steps of how to evaluate each side of the equation.
The associative property of multiplication states that when multiplying three or more numbers, the product remains the same regardless of how the numbers are grouped. In other words, you can change the grouping of the numbers being multiplied without changing the result.
Now, let's evaluate the left side of the equation, (2x)yz:
Step 1: We can start by simplifying the expression within the parentheses: 2x.
Step 2: Now, we multiply 2x by y: (2x) * y = 2xy.
Step 3: Finally, we multiply the result by z: 2xy * z = 2xyz.
Next, let's evaluate the right side of the equation, 2(xy)z:
Step 1: First, we multiply x and y: x * y = xy.
Step 2: Now, we multiply the result by 2(xy)z: xy * 2(xy)z = 2xyz.
As we can see, the left side of the equation, (2x)yz, and the right side of the equation, 2(xy)z, both simplify to 2xyz. Therefore, the equation holds true, and it exemplifies the associative property of multiplication.
Moving on to the commutative property of multiplication:
The commutative property of multiplication states that the order of multiplication operations does not change the result. In other words, you can rearrange the order of the numbers being multiplied without affecting the product.
So, the statement 2(xy)z = (2x)yz doesn't exemplify the commutative property of multiplication because the order of multiplication is different on both sides.